Like you, my instinct is that this would be wrong. Your question is: assuming it harms a child to watch its parents have sex, what exactly is the harm?
Of course, the assumption might be wrong. It's an empirical question. But if it's harmful, what's the nature of the harm?
The obvious first point is that the harm would be psychological, not physical. The perhaps less obvious second point is that if it is harmful, this isn't inevitable, but has a great deal to do with context, expectations, cultural norms and the like.
Imagine a society in which people live in close quarters and privacy is a luxury. It's nor hard to imagine that for purely practical reasons, people would end up being seen by others when they have sex, including by their own children. If the norm in the society was that this was not a big deal, and the normal pattern of behavior was simply to ignore the couple, it's easy to imagine that seeing one's parents have sex wouldn't make for any psychological trauma.
Our society...

Since the word "deontological" covers a lot of territory, I'm going to start with an assumption: I'm assuming that for you, the deontological point of view is non-consequentialist and broadly Kantian: it says that we can't treat people as mere means to an end, even if the end is otherwise a good one. (If that's not what you mean, my apologies.)
If we have a mandatory vaccination rule, on the surface it's all about consequences: it's to protect people from preventable illnesses. But if we make people get their kids vaccinated even if they'd rather not, that sounds like treating them as means to the end of protecting others, even if there are other values at issue from their point of view. So your question is whether letting them opt out by home schooling their children is enough to make the rule acceptable.
We already have such a rule for parents who prefer not to send their children to public school. If that's okay, is there any reason to think a similar rule wouldn't do in the case of vaccinations?
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I don't have a clear fix on the question, but insofar as I do, I don't see how philosophy alone could answer it. You seem to be saying that there's a real-world, repeatable phenomenon: babies in certain situations behave this way rather than that . That may be true—is true, far as I know. But if it's true, there's nothing a priori about it; the opposite behavior is perfectly conceivable and might have been true for all we could have said in advance. I don't see how philosophical analysis could tell us why things turned out one way rather than another. At least as I and many of my colleagues understand philosophy, it doesn't have any special access to contingent facts. A philosopher might come up with a hypothesis, but insofar as the hypothesis is about an empirical matter, it will call for the usual sort of empirical investigation that empirical claims call for.
As for blank slates, philosophy can't tell us by itself whether we're born with blank slates as minds, but as a matter of fact, there...

Let's start with your second sentence: "Biological polygenesis and philosophy of history make it clear that colonialism and destruction of indigenous cultures is not always immoral." A few obvious points. First, biological polygenesis (distinct origins for different races) is not widely accepted among scientists. In fact, far as I know, the evidence points in the opposite direction. Second, even if polygenesis happens to be true, that wouldn't show that colonialism and destruction of indigenous cultures and peoples was okay. Compare: suppose that sometime in the future, humans travel outside the solar system and find intelligent creatures on other planets. Those beings certainly have different origins than we have. But from that it doesn't follow that we would be justified in colonizing them, let alone destroying their culture or killing them. After all, if intelligent aliens make it to earth, that wouldn't make it right for them to colonize us or kill us. And finally, "philosophy of history"...

I agree with my co-panelist that it's hard to peg this as abuse. But I'd like to focus on a somewhat different issue: the word "indoctrination" is being used to mean an illegitimate way of inculcating beliefs. That's fine, and isn't my issue. But the notion of "religious indoctrination" is left unexamined. And so I want to know what counts. In particular, suppose someone brings their children up in a religious tradition: introduces them to the texts and doctrines, participates in the rituals, makes clear that s/he is an adherent, and so on. If indoctrination counts as something bad, is this automatically a case of indoctrination? Surely it depends on the details. Suppose that the religious tradition has admirable moral precepts. Suppose it encourages thoughtful reflection. Suppose it doesn't threaten non-adherents with hellfire and brimstone. There really are such traditions; I know many people who belong to them. The tradition may well include metaphysical claims that you think are just wrong. But is...

Phrases like "child abuse" are most useful if they pack some punch. When we think of child abuse, what comes to mind are such things as deliberate acts of cruelty, gross neglect, causing serious bodily harm, and sexual molestation. All of those are clear cases of child abuse. Whether a child ends up obese, however, is a complicated matter. Two children might eat the same diet, and yet one might end up obese and the other not. Parents may have some control over their children's weight, but the decision that one's child will not become obese might not be easy to act on, and acting on it might have its own unfortunate side effects. This isn't to suggest that childhood obesity is trivial. But obesity is complicated. If it could be easily prevented, and if the way to prevent it was widely understood, then we might say that clear cases of "allowing" one's child to become obese count as a kind of child abuse. As it is, things aren't nearly so straightforward.

The term "child abuse" is loaded enough that I'm going to set it aside. And I'm going to restrict myself mainly to one point. You seem to assume that religion is always a matter of "blind faith" and that if parents bring their children up in a religious tradition, this is inevitably a matter of "programming." But why think that? Isn'tit possible that perhaps you've been a bit indoctrinated (not to say brainwashed) on that point yourself? Some beliefs are blind. That applies to some cases of religious belief and to a good many other kinds of belief as well. But not all beliefs about matters that go beyond the facts need be blind, and this is as true for religion as it is for anything else. The great religious traditions include traditions of argument, reflection, weighing of considerations, and discernment. Not all believers cling to their beliefs for dear life; not all believers believe that they're bound for hell if they have questions or doubts. In fact, for some serious religious people,...

Perhaps we could start with a related question: who owns you? The answer, I'd think, is "No one." You aren't property. You may have obligations and responsibilities to others, but part of the way we think about persons is that they aren't property and shouldn't be treated as such. That suggests that children aren't property either. They have more limited rights and responsibilities than adults do, but they don't belong to anyone in the way that, say, a painting might belong to me. Suppose I own a valuable painting by some important artist -- Cezanne, for the sake of an example. Then though it would be a wasteful and bizarre thing for me to do, I am entitled to do most anything with that Cezanne -- including burning it or using it as a tablecloth. That goes with it's being property. But suppose I have a child. The word "have" here doesn't mean "own." For present purposes, it might best be thought of as meaning "am responsible for," and not just biologically. The child is entitled to be...

I think you've raised a good question, but I do think the issue is a lot more general than religion. In raising children, we convey a great deal to them about our beliefs and values on many things -- including many controversial things. This includes political values, larger ethical values, what sources of information are to be trusted and a good deal more. It's hard to see how we could avoiding doing that, and hard to see why we would want not to. That said, the word "indoctrination" is perhaps the key here. We can raise our children to be more or less thoughtful, more or less open-minded, more or less willing to reason. If we tend to stress thoughtfulness, inquisitiveness, willingness to consider objections to one's own views, then the word "indoctrination" seems less appropriate. Of course, open-mindedness and cognitive flexibility are values that not everyone shares. But what distinguishes them from indoctrination is precisely that they aren't matters of accepting specific doctrines. We...